As is known in the art, impedance matching of radio frequency (RF) circuits and systems is the practice of matching en impedance of one or more ports of a first RF circuit or system to the impedance of one or more ports of a second RF circuit or system to ideally maximize the power transfer or minimize reflections from the ports. For example, it is desirable to match an RF amplifier output impedance to en input impedance of another RE component coupled to the RF amplifier output for the purpose of maximizing power transfer between the RF amplifier and the subsequent RF component.
As is also known, a properly designed transmission line may perform the function of an impedance matching network. One type of transmission line having an impedance matching taper is described by R. W. Klopfenstein in a paper titled “A Transmission Line Taper of Improved Design,” published in the Proceedings of the IRE, page 31-35, January 1956.
Transmission lines provided having a taper in accordance with the aforementioned paper are commonly referred to as “Klopfenstein transmission line tapers” or as “Dolph-Tchebycheff transmission line tapers.” Such transmission line tapers are optimum in the sense that ideally, they provide minimum reflection coefficient magnitudes in a pass band for a specified length of taper. Similarly, for a specified maximum magnitude reflection coefficient in the pass band, an ideal Dolph-Tchebycheff transmission line taper (a/k/a Klopfenstein taper) has a minimum length.
Referring now to FIG. 1, an exemplary transmission line 10 has a first end 10a and a second end 10b and a conventional Klopfenstein transmission line taper extending from the first end to the second end. Such Klopfenstein transmission lines are found in a variety of different RF systems, circuit and devices.
Following the Klopfenstein's technique, the transmission line 10 presents an impedance transformation that closely follows the real axis of a Smith chart. Impedance matching required in practical applications, however, usually contains a reactive component. Thus, deviations from the Klopfenstein equations allow one to transform complex impedances represented on the Smith chart in regions away from the real axis.
FIG. 2 shows one such deviation known in the prior art, where experimentally stretching/shrinking the width and length of a transmission line (e.g. transmission line 10 in FIG. 1) at random locations 22a-22e results in a transmission line 20 having a first end 20a and a second end 20b. It should be noted transmission line 20 includes regions 22a-22e used to shorten the transmission line length and optimize the transmission line for a complex impedance match as is generally known.
While the Klopfenstein transmission line taper (a/k/a the Dolph-Tchebycheff taper) provides good electrical performance characteristics, in certain applications, it is sometimes desirable (or even necessary) to use a matching circuit having a length which is shorter than that provided by a conventional Klopfenstein transmission line taper. At the same time, it is desirable to use a matching circuit having electrical performance characteristics which are substantially the same as those provided by a conventional Klopfenstein transmission line taper.